Eight-Lump Kinetic Modeling of Vacuum Residue Catalytic Cracking in

Article pubs.acs.org/EF

Eight-Lump Kinetic Modeling of Vacuum Residue Catalytic Cracking in an Independent Fluid Bed Reactor Haohua Gao,†,‡ Gang Wang,*,† Chunming Xu,† and Jinsen Gao† †

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China National Institute of Clean-and-Low-Carbon Energy, Shenhua Group Corporation Limited, Beijing 102211, China

‡

ABSTRACT: This study proposes an eight-lump kinetic model to describe the reaction behavior of the vacuum residue (VR) catalytic cracking in a conceptual catalytic cracking process. The proposed lump model has 20 kinetic constants and one for catalyst deactivation, which is specifically suitable for a VR catalytic cracking process. In this reaction system, the VR is divided into three lumps on the basis of the composition of the structure group, so as to expand the application of the model. The experimental data were obtained from a fixed fluidized-bed reactor and a pilot plant. The kinetic constants were estimated using a special program compiled on the basis of Marquardt’s algorithm. The model shows high simulation accuracy, with the predicted yields being in close agreement with the experimental results. In addition, model simulations were performed to determine the effects of two parameters on product yields. By setting the unit characteristic factors, the model was applied to a pilot plant, and the concentration profiles of the components along the reactor were described. two reaction zones. In the first zone, a relatively light hydrocarbon feedstock is contacted with the first catalyst stream comprising the spent catalyst. In the second zone, another relatively heavy hydrocarbon feedstock is contacted with the second catalyst stream comprising freshly regenerated catalyst. Besides, Herbst et al.12 proposed a multiple riser catalytic cracking process, which involves the following processes: (1) conversion of the first hydro-deficient heavy hydrocarbon feedstock in the first riser; (2) conversion of a hydrogen-rich hydrocarbon feedstock in the lower region of the second riser, and (3) feeding a second relatively hydro-deficient heavy hydrocarbon feedstock into the upper region of the second riser. However, no further advancements of these processes have been reported. Recently, our research group developed a conceptual catalytic cracking process on the basis of the reaction characteristics.13 Figure 1 shows the schematic of the conceptual catalytic cracking process proposed by our research group. Contrary to the state-of-the-art practice of the RFCC process, the conceptual catalytic cracking process involves two reactors. Vacuum gas oil (VGO) is cracked in the conventional riser reactor, while VR is converted in the other modified reactor. The objective of the improvement is to weaken the competitive adsorption effect between VGO and VR and provide favorable reaction conditions. Thus far, a number of studies, including prestage feasibility analysis and process parameters, has been conducted on this process.13 However, to the best of our knowledge, there are not many studies on the reaction kinetics, which might actually facilitate the optimization of this process. It is well-known that building a kinetic model is highly imperative to deeply describe the reaction characteristics after

1. INTRODUCTION The recent upsurge in the demand for high value-added petroleum products, together with the worldwide increasing trend for heavier and inferior crude oil supply, has contributed to the increased use of residue feedstock in the refineries.1−4 Fluid catalytic cracking (FCC) is one of the most important technologies in oil refining industries, in which the heavy fractions of the crude oil are converted or cracked into a variety of lighter products.5 Consequently, FCC is being widely used for converting the residues into more useful products,6 especially in countries like China.7 The conventional residue fluid catalytic cracking (RFCC) process involves blending residues, such as atmospheric residue (AR) or vacuum residue (VR), deasphalted oil, aromatic extracts, and so on, into vacuum gas oil (VGO). It is wellknown that the distillation range and physicochemical properties of VR dramatically differ from those of VGO. Compared with VGO, VR usually has a higher molecular weight and boiling point and contains more sulfur and nitrogen heteroatom species that cause poisoning of the acid sites.7−9 Most catalyst contaminant metals in crude oil, such as nickel, vanadium, sodium, and iron, are concentrated in VR, which contributes to more contaminant coke and irreversible deactivation of catalysts. These inherent differences between VGO and VR contribute to their diverse reaction characteristics. However, during the typical RFCC process, VGO and VR are usually premixed and then cracked in one common reactor at the same reaction conditions. Given their diverse reaction characteristics, cracking them in one common reactor ultimately causes a competitive adsorption effect between them, thereby further retarding the reaction.7,10 In order to reduce this retardation effect and improve the product distribution by considering the reaction characteristics of different feedstock used in FCC, some novel FCC processes have been proposed in the literature.11,12 For instance, Harandi et al.11 proposed a multizone catalytic cracking process, which generally comprises © 2014 American Chemical Society

Received: June 4, 2014 Revised: September 2, 2014 Published: September 3, 2014 6554

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of the catalytic cracking processes as well as for the lump kinetic study. Unfortunately, previous studies in this regard have mainly focused on the VGO and heavy oil coking deactivation.7 Only few deactivation models could be applied for pure VR catalytic cracking. Therefore, it is highly imperative to establish a coking deactivation model for the VR catalytic cracking. To this end, this study presents a different eight-lump model for describing the reaction behaviors of pure VR catalytic cracking. Moreover, the relationship between microactivity index and coke content is also investigated, in which the coking deactivation model for VR catalytic cracking has been established. The kinetic parameters have been estimated using a custom program based on the Marquardt’s algorithm. Furthermore, we have also investigated the effects of the two parameters on the product distribution. By setting the unit characteristic factor, the model has been applied to a pilot plant.

2. EIGHT-LUMP KINETIC MODEL 2.1. Model Description. In this study, the VR lump was divided into three sublumps, namely, alkyl carbon lump (CP), naphthenic carbon lump (CN), and aromatic carbon lump (CA). The numerical values of the three lumps (CP, CN, and CA) were determined using the modified Brown-Ladner method based on the data of VR 1H NMR. This well-known method has been commonly used for the structural analysis of petroleum and its fractions.26−28 The detailed values are listed in Table 1. The product was divided into five groups according

Figure 1. Schematic of the conceptual catalytic cracking process.

Table 1. Average Molecular Weight and Initial Values of Eight-Lumps

separately feeding in the different reactors. The catalytic cracking process is a complicated reaction system involving a vast number of molecules. Therefore, it is often extremely difficult to characterize and describe the kinetics at the molecular level.7 Consequently, such complicated reaction systems are usually studied by lumping the large numbers of chemical compounds into several pseudocomponents, according to their boiling points and molecular characteristics.14 To this end, several lump kinetic models, including 3-lump,15 4lump,16 5-lump,17 6-lump,18 7-lump,19 8-lump,20 10-lump,21 11lump,22 13-lump,23 and 14-lump,24 have been proposed in the literature. The majority of these models focus on the VGO or heavy oil, while only a few lump kinetic models focus on pure VR catalytic cracking. Recently, our group worked on the development of a lumping kinetic model with a product distribution for VR catalytic cracking in a fluidized bed reactor.25 The model did not take into consideration the properties of the feedstock. Therefore, the model could not be expanded to describe the reaction behaviors of other VR feedstock. One possible solution to the above-mentioned problem is to divide the feed into several lumps. As it is wellknown, irrespective of the complexity in the composition and molecular structure of VR, the hydrocarbon molecules can be considered an aggregation of alkyl groups, cycloparaffin groups, and aromatic groups. The proportion of these three groups in the hydrocarbon molecule can be represented by the ratio of carbon atoms of the alkyl side chain, naphthenic rings, and aromatic rings on the total number of carbon atoms.22−24 Given this viewpoint, it is simpler and reasonable to divide the VR lump on the basis of their structural group. Furthermore, coking is an inevitable and important process during VR catalytic cracking. Coking tends to reduce the activity of the catalysts and results in the variation of product distribution, given the fact that the deposited coke covers parts of the active sites on the catalyst surface. Therefore, the study of coking deactivation is helpful to an insightful understanding

average molecular weight, (g·mol−1)

initial values

lumps

CQ-VR

JN-VR

CQ-VR

JN-VR

CP CN CA HCO light oil LPG dry gas coke

662 662 662 371a 130 40 16 400b

859 859 859 371 130 40 16 400

0.66 0.15 0.19

0.65 0.06 0.29

a

Molecular weight of HCO reported by Peixoto and Medeiros.29 Molecular weight of coke lump reported by Xu et al.19 and Wang et al.30 b

to their carbon number and boiling point ranges, as follows HCO (350−500 °C), light oil (C5−350 °C), LPG (C3−C4), dry gas (C1− C2), and coke. An eight-lump model with 20 reactions was established, as shown in Figure 2. 2.2. Mathematical Models. The following assumptions were made to develop the mathematical model:14,15 (1) the feedstock vaporizes instantaneously; (2) plug flow for gas and catalyst and the radial dispersion in the reactor are negligible; (3) the reactor is either isothermal or adiabatic; (4) the catalyst deactivation is nonselective. Accordingly, the continuity equation for the reactor can be written as in the following eq 1. ⎛ ∂ρCi ⎞ ⎛ ∂C ⎞ ⎜ ⎟ + G V ⎜ i ⎟ = − ri ⎝ ∂t ⎠x ⎝ ∂x ⎠t

(1)

The reaction rate (ri) is proportional to the molar concentration of lump i (ρ/Ci) and the ratio of the catalyst mass density to the gas volume (ρb/ε), as shown in eq 2. Furthermore, the rate constant ki′ is not a constant, rather it decreases with the deactivation of the catalyst. Accordingly, 6555

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dC 2 P MW (k6 + k 7 + k 8 + k 9 + k10)C 2 Φ =− dX S WHRT

(11)

dC 3 P MW =− (k11 + k12 + k13)C3Φ dX S WHRT

(12)

dC4 P MW =− [ν14k1C1 + ν24k6C2 + ν34k11C3 S WHRT dX − (k14 + k15 + k16 + k17)C4]Φ

(13)

dC5 P MW =− [ν15k5C1 + ν25k10C2 + ν35k13C3 S WHRT dX − (k18 + k19 + k 20)C5]Φ

(14)

dC6 P MW =− (ν16k 2C1 + ν26k 7C2 + ν46k17C4 + ν56k18C5)Φ dX S WHRT (15) Figure 2. Kinetic scheme of the eight-lump model.

ri = ki′(ρCi)

dC 7 P MW (ν17k4C1 + ν27k 9C2 + ν47k15C4 + ν57k 20C5)Φ =− dX S WHRT (16)

ρb (2)

ε

Substituting eq 2 in eq 1, we can deduce the following eq 3. ρ ⎛ ∂ρCi ⎞ ⎛ ∂C ⎞ ⎜ ⎟ + G V ⎜ i ⎟ = − ki′(ρCi) b ⎝ ∂t ⎠x ⎝ ∂x ⎠t ε

C8 = (1 − C1M1 − C2M 2 − C3M3 − C4M4 − C5M5 − C6M6) /M 7 (3)

where the stoichiometric coefficient, vij, is equal to MWi/MWj. The concentration of the coke’s lump C8 can be calculated by using a mass balance. 2.3. Catalyst Deactivation Model. For the kinetic studies of lumping models during catalytic cracking, the catalyst deactivation function (Φ) is usually described by a function that depends on the time-on-stream (TOS, the residence time of catalyst) or catalyst coke content (COC). Previous studies in this regard have predominantly adopted the catalyst deactivation functions that depend on TOS. However, functions depending on COC are much more appropriate for VR catalytic cracking, given the fact that coking is one the most important reactions during VR catalytic cracking.31,32 Therefore, in this paper, a deactivation function depending on COC was adopted and could be described as7

In the case of the steady-state fluidized-bed reactors, the time partial derivative is zero for gas-phase plug flow. Accordingly, replacing x with the dimensionless length X = x/L, eq 3 can be rewritten as follows:

ρ G V dCi = − ki′(ρCi) b L dX ε

(4)

By definition, GV = ((SWHρbL)/ε), and hence, eq 4 can be written as

dCi 1 =− k i′(ρCi) dX S WH

(5)

Here, assuming that the oil gas in the reactor is an ideal gas,

ρ=

P MW RT

f (CC) = Φ = (1 + βCC)−M

(6)

n

MW =

∑i = 0 Ci MWi n

∑i = 0 Ci

=

n

(7)

where MW is the average molecular weight of the oil gas and MWi is the average molecular weight of lump i. In this paper, although the VR lump was divided into three lumps (CP, CN, and CA), we assume that the molecular weights of them are equal to that of VR.22 The average molecular weights of the lumps in the eight-lump model are summarized in Table 1. The actual rate constant k′i is equal to the product of the intrinsic rate constant ki and the catalyst deactivation function (Φ), as is shown in the following eq 8.

ki′ = ki Φ

(8)

Hence, eq 9 can be deduced from eqs 5−8, as follows:

dCi P MW =− kiCi Φ dX S WHRT

(9)

According to the reaction network of the eight-lump, the mathematical equations of the kinetic models can be written as follows: dC1 P MW =− (k1 + k 2 + k 3 + k4 + k5)C1Φ dX S WHRT

(18)

where β and M are the COC dependent parameters that can be determined by coke deposition experiments. To this end, the coking experiments were carried out in a fixed fluidized bed reactor, which is a batch system operated in the fluidized mode. In each experiment, the commercial equilibrium catalyst LVR60R and Changqing (CQ) VR were used and the details have been described elsewhere.25 The reaction conditions are as follows: the reaction temperature is 500 °C, catalyst loading is 60 g, and the weight hourly space velocity (WHSV) is 25 h−1; the feeding time ranges from 1 to 40 s. Eight spent catalysts with different coke contents were collected. The coke content on catalysts was determined by the high frequency infrared carbon sulfur analyzer HIR-944B, and their microactivity was tested on the basis of the ASTM D5154-2003 method. Their detailed values are listed in Table 2. The COC dependent parameters in eq 18 were determined through the leastsquares regression analysis of the experimental data, and the R-squared was up to 0.99 as shown in Figure 3. Accordingly, the parameters were determined to be β = 0.93 and M = −0.68. Figure 3 reveals the variations in deactivation functions for different feedstock catalytic crackings.7 As is seen, the microactivity tends to differ for the same coke content of a catalyst. The observed variation follows the sequence: VGO > heavy oil > VR. Compared to VGO and heavy oil, VR contains large-sized and refractory polycyclic aromatic hydrocarbons. Thus, the reactants can access the inner pores of zeolite only after thermal cracking on the external of the catalyst substrate. Thus, for the same coke content of the catalyst, there is a decrease in

1 ∑i = 0 Ci

(17)

(10) 6556

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operated in the fluidized mode. The application simulation experiments were performed in a technical pilot scale riser with a throughput of 2.0 kg/h and a catalyst holdup of 12 kg. Details on the specifications of the equipment and the experimental data have been published elsewhere.13,25 3.1. Estimation of Kinetic Parameters. In order to determine the kinetic constants, a program was compiled in Matlab. The kinetic constants of the eight-lump model at 460, 480, 500, and 520 °C were estimated using the experimental data obtained from CQ-VR catalytic cracking in a fixed fluidized bed reactor. The values of kinetic constants thus obtained are listed in Table 3. In the case of the CP lump cracking, the rate constant k5 was found to be much larger than the other rate constants. More quantitatively, the following trend was observed in the rate constants: k5 (CP to light oil) > k2 (CP to LPG) > k4 (CP to dry gas) > k3 (CP to coke) > k1 (CP to HCO). This indicates that the main product of CP cracking is the light oil. On the other hand, in the case of the lump CN cracking, the rate constant k10 was found to be larger than the other rate constants. The variation trend of rate constant was: k10 (CN to light oil) > k6 (CN to HCO) > k8 (CN to coke) > k7 (CN to LPG) > k9 (CN to dry gas). However, k10 is slightly smaller than k5. This implies that CN is also mostly converted into light oil during the catalytic cracking process. The aromatic carbons do not undergo ring-opening reactions, which would not have produced small molecular products, LPG, and dry gas. The variation trend of rate constant is k13 (CA to light oil) > k12 (CA to coke) > k11 (CA to HCO). At various temperatures, the reaction rate ratios of CA (k13/k11 and k13/k12) are less than that of CP (k5/k1 and k5/k3) and CN (k10/k6 and k10/k8). This indicates that the light oil selectivity of CA lump cracking is lower than the other lump cracking. In the case of coke and heavy oil production, the variation sequence of the rate constant is k12 (CA to coke) > k8 (CN to coke) > k3 (CP to coke) and k11 (CA to HCO) > k6 (CN to HCO) > k1 (CP to HCO), respectively, where k12 and k11 are much larger than the others. This indicates that the aromatic carbons are the main

Table 2. Coke Contents on Catalyst vs Relative Microactivity number

feeding quantity, g

time, s

coke content, wt %

relative microactivity

1 2 3 4 5 6 7 8

0.50 1.61 3.08 5.13 9.15 13.25 20.34 20.26

1 3 6 10 18 26 32 40

0.16 0.40 0.66 1.01 1.33 1.78 2.03 2.44

0.89 0.80 0.73 0.63 0.58 0.48 0.48 0.46

Figure 3. Catalyst deactivation functions for different feed catalytic cracking. the catalytic coke, which in turn has a significant effect on the corresponding microactivity. With an increase in the coke content of the catalyst to 1.2 wt %, the relative microactivity decreases to 0.6.

3. RESULTS AND DISCUSSION The VR catalytic cracking of CQ and Jinan (JN) was conducted in a fixed fluidized bed reactor. The reactor is a batch system Table 3. Kinetic Rate Constants

reaction temperature (°C) −3 −1

−1

reaction network

kinetic rate constants ((kg·m ) ·h )

460

480

500

520

CP → HCO CP → LPG CP → coke CP → dry gas CP → light oil CN → HCO CN → LPG CN → coke CN → dry gas CN → light oil CA → HCO CA → coke CA → light oil HCO → light oil HCO → dry gas HCO → coke HCO → LPG light oil → LPG light oil → coke light oil → dry gas

k1 k2 k3 k4 k5 k6 k7 k8 k9 k10 k11 k12 k13 k14 k15 k16 k17 k18 k19 k20

0.15 9.04 0.45 0.76 42.43 4.98 2.46 4.86 0.39 41.34 12.06 20.20 20.94 1.76 0.49 0.23 1.44 0.03 0.15 0.03

0.19 11.19 0.51 0.94 46.13 6.05 3.13 5.49 0.49 45.11 13.80 21.87 26.02 2.62 0.68 0.27 2.07 0.04 0.19 0.04

0.24 13.69 0.58 1.15 49.94 7.29 3.95 6.16 0.61 48.99 15.69 23.57 31.96 2.96 0.81 0.38 2.27 0.05 0.24 0.05

0.30 16.60 0.66 1.39 53.84 8.70 4.92 6.87 0.75 52.99 17.72 25.32 38.85 3.33 0.93 0.43 2.67 0.06 0.28 0.06

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cause underlying the production of coke and heavy oil, which is consistent with the result reported in the literature.7 Table 4 lists the frequency factors and apparent activation energies calculated using the Arrhenius equation. As is seen, Table 4. Frequency Factors and Apparent Activation Energies reaction network CP → HCO CP → LPG CP → coke CP → dry gas CP → light oil CN → HCO CN → LPG CN → coke CN → dry gas CN → light oil CA → HCO CA → coke CA → light oil HCO → light oil HCO → dry gas HCO → coke HCO → LPG light oil → LPG light oil → coke light oil → dry gas

frequency factor ((kg·m−3)−1·h−1) A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20

1436.55 29436.77 64.07 2643.87 1012.32 8349.86 25591.10 492.75 2121.76 1118.79 2018.28 407.48 78433.00 5900.55 2348.19 1644.02 3210.88 200.52 487.80 364.45

activation energy (kJ·mol−1) E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14 E15 E16 E17 E18 E19 E20

56.05 49.39 30.24 49.80 19.36 45.36 56.45 28.22 52.41 20.16 31.25 18.35 50.20 49.06 51.46 54.31 46.65 53.69 49.13 57.04

Figure 4. Comparison between the experimental yields (points) and the predicted yields (line) for CQ-VR in the fixed bed at 480 °C.

Besides, the secondary reaction rates are also relatively smaller. These results indicate that VGO has good crack-ability and favors secondary reaction due to the high content of CN and CP carbons. In contrast to the residual oil catalytic cracking, the rate constants of VR catalytic cracking are closer to each other. However, the ratio of primary and secondary reactions for generating light oil is higher. This indicates that the light oil lump favors the reaction path for VR catalytic cracking (VR → light oil). Table 6 lists the apparent activation energies of VGO, residual oil, and VR catalytic cracking. The activation energy for generating light oil (32.6−38.5 kJ·mol−1) during VGO catalytic cracking is lower than that of residual oil and VR catalytic cracking. Moreover, the activation energy for generating coke during VGO catalytic cracking (81.5 kJ/mol) is far less than that of VR catalytic cracking (18.4 kJ/mol). These results substantiate the fact that the VGO and VR have diverse reaction characteristics and hence require different reaction operation strategies. Therefore, a better product distribution can be realized via separate feeding.13,25 3.2. Prediction of Product Yields. One of the important applications of the kinetic model is to predict the product distribution. Some fundamental information can be obtained from the model for the optimization of the reaction process. The forthcoming section presents some simulation results and related discussions. Figure 5 shows the predicted relationship between product yield and the reaction temperature at a WHSV of 20 h−1 and CTO of 6 and LVR-60R as the catalyst for JN-VR. The details of the feedstock have been described elsewhere.13,25 It was clearly observed that the simulation values were close to the experimental ones. This indicated that the eight-lump kinetic model can fit the experimental data well. With an increase in the reaction temperature, the light oil yield tends to decrease, while the yields of dry gas and LPG increase continuously. This trend is in agreement with serial kinetics. The temperature, as a main process parameter, significantly influences the product distribution caused by the thermodynamics of the catalytic cracking reactions. Catalytic cracking being an endothermic reaction is obviously favored by a higher reaction temperature. However, the product distribution of a parallel-series reaction is closely associated with the reaction depth. The excessive conversion caused by high reaction temperature will lead to the generation of undesirable products, such as dry gas and coke.

most activation energies are in the range of 40−60 kJ·mol−1, close to the values reported in the literature14 but lower than those reported for thermal cracking (210−290 kJ·mol−1).7 This result confirms the practical feasibility of dividing the VR into CP, CN, and CA lumps, consistent with the catalytic cracking reaction mechanism. The activation energy E5 (CP to light oil) is closer to E10 (CN to light oil) but far less than E13 (CA to light oil). This shows that the CP and CN can readily be converted into light oil, while the conversion of CA is rather difficult. Nevertheless, the activation energies of generating coke and heavy oil are just the opposite. More quantitatively, E12 (CA to coke) < E8 (CN to coke) ≈ E3 (CP to coke) and E11 (CA to HCO) < E6 (CN to HCO) < E1 (CP to HCO), indicating that the aromatic carbons are more inclined to generate coke and heavy oil. Moreover, the apparent activation energies for cracking CN and CP into gas (E2, E4, E7, E9) are larger than that for generating light oil (E5, E10). This shows that, with an increase in the reaction temperature, the reaction rate for producing gas increases more quickly than in the other reactions. Therefore, a relatively low temperature is favorable for the process producing liquid products. Figure 4 shows the comparison of the experimental yields (points) and those predicted by the model (line) for the catalytic cracking of CQ-VR at 480 °C. As is seen, the predicted yields are almost closer to the experimental ones. This indicates that the eight-lump kinetic model adopted in this study fits well with the experimental data and that the predicted results are reliable. Table 5 lists the kinetic rate constants of VGO,22 residual oil,19 and VR catalytic cracking. Compared with the VGO catalytic cracking, the primary reaction rates of VR catalytic cracking are lower by more than an order of magnitude. 6558

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28.5−86.5 0.5−14.0 2.9

LFO → gasoline LFO → coke gasoline → coke

secondary reaction

RFO: residual oil; HFO: heavy fuel oil; LFO: light fuel oil; gas: LPG and dry gas.

56.0−155.0 77.8−144.1 12.7−41.8

HFO → LFO HFO → gasoline HFO → gas + coke

primary reaction

−1

6559

a

−1

32.6 46.0 124.1

LFO → gasoline LFO → coke gasoline → coke

secondary reaction

RFO: residual oil; HFO: heavy fuel oil; LFO: light fuel oil; gas: LPG and dry gas.

38.5 32.6 81.5

HFO → LFO HFO → gasoline HFO → gas + coke

primary reaction

activation energy (kJ·mol )

reaction network

items

a

VGO 11-lump22

a

RFO → HFO RFO → LFO/gasolie RFO → gas RFO → coke HFO → LFO/gasolie HFO → gas HFO → coke LFO → gas + coke

reaction network

14.9 5.8−11.7 0.4−3.6 11.6 0.9−5.8 0.01−0.1 0.3